A145534 a(n) is the number of numbers removed in each step of Eratosthenes's sieve for 7!.

2519, 839, 335, 191, 104, 79, 57, 49, 39, 31, 27, 21, 18, 17, 14, 9, 7, 5, 3

Offset

1,1

Comments

Number of steps in Eratosthenes's sieve for n! is A133228(n).

Number of primes less than 7! is 7! - (sum all numbers in this sequence) - 1 = A003604(7).

Links

Table of n, a(n) for n=1..19.

Maple

A145534 := {$(1..7!)}: for n from 1 do p:=ithprime(n): r:=0: lim:=7!/p: for k from 2 to lim do if(member(k*p, A145534))then r:=r+1: fi: A145534 := A145534 minus {k*p}: od: printf("%d, ", r): if(r=0)then break: fi: od: # Nathaniel Johnston, Jun 23 2011

Mathematica

f3[k_Integer?Positive, i_Integer?Positive] := Module[{f, m, r, p}, p = Transpose[{r = Range[2, i], Prime[r]}]; f[x_] := Catch[Fold[If[Mod[x, #2[[2]]] == 0, Throw[m[ #2[[1]]] = m[ #2[[1]]] + 1], #1] &, If[Mod[x, 2] == 0, Throw[m[1] = m[1] + 1]], p]]; Table[m[n] = -1, {n, i}]; f /@ Range[k]; Table[m[n], {n, i}]]; nn = 7; kk = PrimePi[Sqrt[nn! ]]; t3 = f3[nn!, kk] (* Bob Hanlon (hanlonr(AT)cox.net) *)

Crossrefs

Cf. A003604, A133228, A145532-A145540.

Sequence in context: A215197 A250694 A250679 * A166931 A131662 A068352

Adjacent sequences: A145531 A145532 A145533 * A145535 A145536 A145537

Keyword

fini,full,nonn

Author

Artur Jasinski with assistance from Bob Hanlon (hanlonr(AT)cox.net), Oct 14 2008

Status

approved